Quadratic Function Relationship Research Articles

Centrifugal motion of an optically levitated particle.

Levitated optomechanical systems experience a tremendous development on detecting weak force and torque with the center of mass motion and rotation of the levitated particle. Here the levitated optomechanical system is established on a rotating platform, and the centrifugal motion of the particle is observed after rotating the optical platform. The centrifugal displacement of the particle is experimentally proven to show a quadratic function relation with the rotation speed, and the stiffness of the trap and the mass of the levitated particle are obtained from it separately. Furthermore, the centrifugal motion makes the particle deviate from the laser focus center, which would decrease the particle spin speed. These results will help to understand the centrifugal motion and fully consider this effect when the optomechanical system rotates.

DISCRETE ELEMENT SIMULATION FOR CRACK FRACTAL EVOLUTION LAWS ASSOCIATED WITH SLICING MINING IN SUPER THICK COAL STRATUM

This paper presents an approach of combining fractal geometry theory and UDEC discrete element numerical simulation method to study the fractal evolution law of mining-induced fracture of overburden rock. It can be applied to quantitatively evaluate development characteristics of mining fracture network in weakly consolidated overburden under the high-intensity mining in the western mining area. The research result indicates the following findings. The development and expansion of overlying rock fractures have good self-similarity under high-intensity mining conditions and the fractal dimension is between 0.461 and 1.488. The law of evolution can be divided into four stages including the dimensionality rapidly increasing stage,quickly reducing stage,stable stage,and periodically varying stage. In addition,the fractal dimension at each stage and the number of mining meet the logarithmic relationship,linear relationship and quadratic function relationship,respectively. With slice mining in huge coal stratum,the fitting curve of fractal dimension shows a high degree of similarity,has a certain periodicity,and shows a power function relationship. The research results provide scientific basis and technical reference for safe mining in western mining area and protection of water resources.

Numerical study on static properties and failure mechanisms of landing assembled Chinese solar greenhouses

To satisfy the requirements of fast construction, environmental protection and cost effectiveness, a new type of landing assembled Chinese solar greenhouse (CSG) was proposed recently. This kind of CSG consists of south roofs, north roofs and columns. In this study, a 2-D finite element model of a landing assembled CSG was developed. The in-plane structural responses of this greenhouse were investigated using ANASY. Firstly, the static properties of the CSG structure were studied under six load cases and the most unfavorable load case was obtained. Secondly, under the most unfavorable load case, the in-plane elastic-plastic failure mechanisms of the structure were investigated. Lastly, the effects of north roof angle, column angle, span width and section modulus on the load-carrying capacity of this type of CSG structure were discussed. The results showed that this type of CSG structure has a good load-carrying capacity to satisfy the design requirements. Snow load is the main control load and the structure is more sensitive to non-uniform snow load. Under non-uniform snow load, the global in-plane failure of the greenhouse occurs owing to in-plane elastic-plastic buckling produced by axial compression and bending moment, and the bending moment plays a more important role in the failure of the structure than the axial force. When other building parameters are fixed, the landing assembled CSG structure with a larger north roof angle and smaller column angle has a higher ultimate load-carrying capacity. The ultimate load-carrying capacity and span width present a quadratic function relationship (R2 = 0.982). The section modulus has a significantly positive linear relationship to the ultimate load-carrying capacity (R2 = 0.999). Analytical results will provide a reference for the theoretical research and engineering design of a landing assembled CSG structure.

Influence of Glass Powder on Rheological Properties of Ultra-High Performance Concrete Paste

Replacing cement and silica fume with glass powder to prepare ultra-high performance concrete (UHPC) is beneficial to solve the ecological problem in the field of civil engineering, but the technologies of preparation, transportation, pumping, and hardening of UHPC mainly relate to its rheological property. Therefore, this paper studied the influence of glass powder on the rheological properties of UHPC paste by performing the flow and the rheological test. Experimental results showed that when the cement and silica fume partially replaced by glass powder, the UHPC paste appears shear thickening, yield stress, plastic viscosity, and area of hysteresis loop decrease. This means that mixing glass powder can somehow inhibit the problems of segregation and bleeding of UHPC during pumping. In this manner, the dosage of the superplasticizer in UHPC is appropriately reduced, the filling capacity of UHPC during pouring is improved, and the energy required for UHPC in the pumping process is weakened. Compared with replacing cement, replacing silica fume with glass powder significantly increases the shear thickening and fluidity of UHPC paste, and at the same, reduces its yield stress and plastic viscosity. This indicates that the construction performance of UHPC is greatly improved with the replacement of silica fume. The fluidity and yield stress of UHPC paste satisfy the quadratic polynomial function relationship, and the replacement of cement and silica fume with glass powder should be less than 33% and 50%, respectively. Under this condition, the rheological properties of the UHPC paste are greatly improved and result in little negative impact on the mechanical properties of UHPC.

Field Test Research on Red Clay Slope under Atmospheric Action

By embedding water content sensors and pore water pressure sensors inside the red clay slope on-site in Guiyang, Guizhou, shear tests were performed on soil samples at different depths of the slope under different weather. The changes of water content, pore water pressure, and shear strength index of the slope inside the slope under the influence of the atmosphere were tracked and tested, and the failure characteristics and evolution of the red clay slope were analyzed. It is believed that the depth of influence of the atmosphere on red clay slopes is about 0.7 m, rainfall is the most direct climatic factor leading to the instability of red clay slopes, and the evaporation effect is an important prerequisite for the catastrophe of red clay slopes. The cohesion and internal friction angle of the slope soil have a good binary quadratic function relationship with the water content and density. The water content and density can be used to calculate the cohesion and internal friction angle. Failure characteristics of red clay slopes: the overall instability failure is less, mainly surface failure represented by gullies and weathering and spalling, and then gradually evolved into shallow instability failure represented by collapse and slump. The damage evolution law is as follows: splash corrosion and surface corrosion stage⟶ fracture development stage⟶ gully formation stage⟶ gully development through stage⟶ local collapse stage⟶ slope foot collapse stage.

Curvilinear relationship between emotional labour and work engagement in nurses: A correlational study.

To examine if there was a curvilinear relationship between emotional labour and work engagement in Chinese nurses. Emotional labour has both positive and negative effects on work engagement, but the curve relationship between the two has not been tested. Correlational design. Multi-stage stratified random sampling was used to recruit samples, and 528 nurses from 5 tertiary first-class general hospitals were recruited in Henan Province. Data were collected by using Hong and Kim's Emotional Labor Scale for nurse and the Utrecht Work Engagement Scale-9. Curve estimation was used to explore the functional model between emotional labour and work engagement. Results were reported according to the STROBE Statement. The three dimensions of emotional labour, 'emotional control effort in profession', 'patient-focused emotional suppression' and 'emotional pretense by norms', had a function relationship of quadratic (R2 =.57, p<.001), quadratic (R2 =.569, p<.001) and cubic (R2 =.238, p<.001), respectively, with work engagement. There was a one-way increasing quadratic function relationship between 'emotional control effort in profession' and work engagement. However, 'patient-focused emotion suppression' and 'emotional pretense by norms' had an inverted U-shaped curve relationship with work engagement. Below the moderate level, 'patient-focused emotion suppression' and 'emotional pretense by norms' were positively related to work engagement. After a certain level, they were negatively related to work engagement. Our results may provide evidences to manage nurses' emotional labour and improve their work engagement. It seems that encouraging or training nurses to learn and master more strategies of emotional control may improve work engagement. Moreover, nursing managers should fully recognise the positive and negative effects of different levels of emotional suppression and emotional pretense on work engagement, so as to develop targeted management strategies.

LNMR experimental study on the influence of gas pressure on methane adsorption law of middle-rank coal

In order to reveal the influence of gas pressure on the gas adsorption law of middle-rank coals, four groups of typical middle-rank coals in China were used as the research objects, using saturated, centrifugal, drying equipment and Low-field Nuclear Magnetic Resonance (LNMR) system to carry out coal samples. The pore structure characterization test and the isotherm adsorption test under different gas pressure were carried out. First, the coal sample's pore size distribution, pore roar distribution, porosity and permeability and other parameters were analyzed. Then, the gas adsorption isotherm process was quantitatively studied based on the established relaxation time (T2) spectrum area conversion model. Finally, the relationship between gas pressure and gas adsorption in coal reservoir was discussed. The experimental results show that the pore structure of middle-rank coal is mainly composed of small pores, and a small number of large pores are distributed. Middle-rank coal has low permeability and good gas storage capacity. Under the same gas pressure, with the increase of adsorption time, the gas adsorption amount gradually increased, and the gas adsorption increment gradually decreased. After 7 h, the adsorption equilibrium is reached. Under different gas pressure, the gas pressure has a proportional relationship with the initial gas adsorption speed, which conforms to the Langmuir adsorption theory with the amount of adsorbed gas, and has a quadratic function relationship with the amount of non-adsorbed gas. When the gas pressure is higher than 2.4 MPa, the time required to reach adsorption equilibrium is shortened to 5 h. Gas pressure has no obvious effect on the micropore structure of middle-rank coal, but it will promote the expansion of middle-large pore structure, and its expansion effect is enhanced with the increase of gas pressure.

The impact of surface air leakage on coal spontaneous combustion hazardous zone in gob of shallow coal seams: A case study of Bulianta Mine, China

Determining the coal spontaneous combustion hazardous zone is of great significance to the fire prevention and extinguishing work of the gob. In this paper, considering the actual situation of the residual coal in the gob of the Bulianta Mine, a spontaneous combustion characteristics test of the water immersion coal (S180) and raw coal (S0) was carried out. According to the experimental results, and considering the air leakage from surface cracks, a three-dimensional model of coal spontaneous combustion in shallow coal seams gob is established, and the correctness of the model is verified by on-site measured data. Then, the model is used to study the effect of different surface air leakage conditions on the hazardous zone of coal spontaneous combustion in the gob of shallow coal seams. Surface air leakage volume increased from 0% to 12% of the working face air volume, and the maximum oxygen concentration in the overlying gob increase of nearly 30 times; the maximum wind velocity increase of 14 times. Even so, there is no coal spontaneous combustion hazardous zone that satisfies both wind velocity and the oxygen concentration in the overlying gob. In the gob of the lower coal seam, with the increase of surface air leakage, coal spontaneous combustion hazardous zone move to the air intake side and deep part of the gob, the maximum width gradually increases; and area increases first, then decreases, which has a quadratic functional relationship with the surface air leakage.

Simulation of coal microstructure characteristics under temperature-pressure coupling based on micro-computer tomography

The distribution of pore-fracture structure in coal directly affects the storage and migration characteristics of fluids. Simultaneously, under the condition of high buried depth, the coal structure is further changed by the temperature-pressure coupling. To study the pore size distribution of coal and the deformation characteristics of different pore-fracture structures under temperature-pressure coupling conditions, six different coal structure models are constructed using three-dimensional computer tomography reconstruction in this work. The box-counting algorithm is used to calculate the fractal dimensions of the pore-fracture structure and pore clusters in different pore sizes of coal. In the meantime, the fractal characteristics of the pore structure in different pore sizes are analyzed. Based on the coal structure model, a linear elastic deformation model under the temperature-pressure coupling is constructed. Moreover, the relationship of porosity and fractal dimension with the deformation of models is studied. The research results show that the porosity positively correlated with fractal dimension. The changes of pore volume fraction and fractal dimension in each pore size distribution range are consistent. Under the temperature-pressure coupling condition, both the model porosity and fractal dimension exhibit a quadratic function relationship with deformation. The deformation analysis of the three-dimensional models and two-dimensional cross-sections show that as the porosity and fractal dimension increase, the coal body deformation exhibits a trend of first decreasing and subsequent increasing. Low fractal dimension and high porosity could increase the model deformation. The research results can afford a theoretical basis for the study of coal structure characteristics under complex conditions.

Experimental study on temperature difference between the interior and surface of Li[Ni1/3Co1/3Mn1/3]O2 prismatic lithium-ion batteries at natural convection and adiabatic condition

Abstract The internal temperature of the battery is important for the design of battery thermal management and battery safety; however, it is difficult to be tested and seldom studied. A method of embedding thermocouples inside a prismatic L i [ N i 1 / 3 C o 1 / 3 M n 1 / 3 ] O 2 (NCM) lithium-ion battery was developed to study the temperature inconsistency between the battery interior and the surface. Six thermocouples were embedded in the interior and six were attached to the surface of the battery. First, the feasibility of the embedding-thermocouples method was verified by comparing the capacity, resistance, temperature etc. between the batteries with and without embedded thermocouples. Then 1C and 2C charging and discharging experiments were carried out under the adiabatic condition in an Accelerating Rate Calorimeter (ARC). 1C−5C rates of charging and discharging experiments were executed under the natural convection condition. The temporal and spatial temperature varieties of battery interior and surface were analyzed. The experimental results show that under the adiabatic condition, the temperature difference (TD) between the interior and surface of the battery was small, only 1.7 °C at 1C discharge rate and 3.1 °C at 2C discharge rate. However, under the natural convection condition, the maximum TD reached 11.3 °C at 5C discharge rate. The TD among the six internal temperature measurement points was small for all cases, which means a good uniform temperature distribution inside the battery. In addition, through experiment-data analysis, a near linear relationship was found for the battery internal and external temperature. The effect of the current rates on the maximum temperature and the maximum temperature difference was also studied. The results showed that a good quadratic function relationship was observed for both the maximum temperature and the maximum TD.

Experimental Study on Main Physical Parameters Controlling Shear Strength of Unsaturated Loess

It is particularly important to study the strength of unsaturated loess, and its accurate determination is crucial to the stability analysis of soil slope and foundation and calculation of earth pressure. In order to reveal the control mechanism of physical parameters on the shear strength of unsaturated loess, the intact and remolded loess were used as the research object; sandy silt, quartz flour, and quartz sand were used as contrast; the systematic direct shear tests of unsaturated loess, sandy silt, and quartz sand under different conditions of water content, dry density, and clay content were carried out. The results show that the cohesion, internal friction angle, and shear strength of unsaturated loess piecewise functionally decrease with the increase of water content, its shear strength increases linearly with the increase of dry density, and its internal friction angle shows an upward quadratic function relation with the increase of clay content. The law results of comparing sandy silt, quartz flour, and quartz sand with loess considering water content and dry density are the same; therefore, the equation of shear strength of unsaturated loess is proposed for practical engineering reference, and by the first derivative analysis of the equation, it is feasible to determine the control proportion of the three parameters on the shear strength of unsaturated loess. A stage-like difference between the three control proportions is observed, depending on the combination variations of water content and clay content.

Experimental study of pore characteristics and radon exhalation of uranium tailing solidified bodies in acidic environments.

The pore characteristics and radon exhalation of uranium tailings solidified in an acid environment were investigated in this study. Tailings from the beach of a uranium tailing reservoir in the acid rain area of Central China were selected as samples and solidified with cement, slag powder (GGBS), metakaolin (MK), or slag powder and metakaolin (GM), then immersed in simulated acid rain solution for 60 days. The transverse relaxation time T2 distribution and porosity of each solidified sample before and after immersion were measured by nuclear magnetic resonance (NMR) and the cumulative radon concentration before and after immersion was measured by a RAD7 radon meter. The experimental results show that the nuclear magnetic resonance T2 distribution curve shifts to the left, the peak amplitude decreases, and the pores in the sample gradually shrink as the admixture content increases. The porosity and radon exhalation rate of solidified samples also appear to decrease gradually as admixture content increases; a quadratic function relationship was observed between porosity and radon exhalation rate. The pore size and effective pore volume of solidified samples increase as immersion time increases, while the radon exhalation rate increases and the pore volume gradually increases. The results of this study may provide a sound theoretical basis for the solidification treatment of uranium tailings in engineering practice.

Effect of Thermal Parameters on Hydration Heat Temperature and Thermal Stress of Mass Concrete

To explore the influence of concrete thermal parameters on the hydration heat temperature and thermal stress of mass concrete, four feature positions of a dam foundation were chosen to analyze the changing process of temperature and stress by varying the thermal parameters, including the thermal conductivity, specific heat, surface heat diffusion coefficient, temperature rise coefficient, solar absorption coefficient, and thermal expansion coefficient. Some conclusions were obtained as follows. Increasing the thermal conductivity and reducing the specific heat and temperature rise coefficient of concrete can effectively reduce the maximum temperature of the central concrete structure. Increasing the solar absorption coefficient, specific heat, and thermal expansion coefficient and reducing the thermal conductivity, surface heat diffusion coefficient, and temperature rise coefficient of concrete can reduce the maximum principal tensile stress in the structure to a certain extent. The maximum principal tensile stress at different positions of the structure has a linear functional relationship with the thermal conductivity, specific heat, and thermal expansion coefficient and has a quadratic function relationship with the surface heat diffusion coefficient, temperature rise coefficient, and solar absorption coefficient. Besides, this study also proposed a series of related anticracking measures. This study was expected to provide a theoretical reference for the design, construction, and cracking disease prevention of mass concrete structures.

Silting thickness analysis of regular desilting in rectangular and trapezoidal channel

Silting in river is a dynamic process, so it needs to regular desilting. At present, underwater siltation monitoring is still in its early days and based on experience. This paper puts forward the criterion of discrimination, in which the flood discharge section is decreased by 20%. It used the method of steady uniform flow in open rectangular and trapezoidal channel for calculation. The results show that reference values of dredging thickness in different section forms were determined. Siltation thicknesses of rectangular channel are linearly related to water depth. And the reduction rate of trapezoidal channel has a quadratic function relation with silting thicknesses. They were proportional to channel width and their rates trended to mitigation when the bottom width and flood depth were constant. In addition, the reference value of dredging thickness should be determined by combining with the bottom width, surface width, water depth and other actual situation.

Study on deformation evolution law of coal under asymmetric loading by digital image correlation.

In this paper, the digital image correlation was innovatively applied to study the deformation and damage process of raw coal and briquette under a complex stress environment. The results show that under symmetrical loading, briquette coal shows tensile failure and that the strain field goes through three stages. The raw coal shows shear failure; the stage characteristic of the strain field is not obvious. Under asymmetric loading, the strain field evolution of raw coal and briquette shows three characteristic stages, but the briquette is more likely to form a localization phenomenon. The displacement value of the crack in the shear direction is greater than that in the tension direction, so the raw coal and briquette mainly undergo shear failure. The localized starting stress is determined by the defined statistical index function, and the localized starting stress of the raw coal and the briquette coal has a quadratic function relationship with the asymmetric coefficient.

Experimental Investigation on the Energy Storage Characteristics of Red Sandstone in Triaxial Compression Tests with Constant Confining Pressure

The elastic energy stored in deep rock in three-dimensional stress environment is the energy source of rockburst. To investigate the energy storage characteristics of deep rock under different confining pressures, a series of triaxial single-cyclic loading-unloading compression tests were conducted on red sandstone specimens under eight confining pressures. The input energy density, elastic energy density, and dissipative energy density of the specimen in axial, circumferential, and total directions can be obtained by the area diagram integration method. The results show that the input energy density in the axial direction accounts for the largest logarithmic proportion of the total input energy density, and the relationship between all energy density parameters and unloading level can be described by quadratic function. In the axial direction, there is a linear function relationship among elastic energy density, dissipative energy density, and input energy density. In the circumferential direction, there is a quadratic function relationship among elastic energy density, dissipative energy density, and input energy density. For the total energy density parameters of the rock specimen, the relationship among elastic energy density, dissipative energy density, and input energy density conforms to the quadratic function. According to the above correlation function, the elastic energy stored in deep rock under different confining pressures can be accurately obtained, which provides a foundation for studying the mechanism of rockburst under three-dimensional unloading from the energy perspective.

Chloride diffusion behavior of coral aggregate concrete under drying-wetting cycles

This study investigated the chloride diffusion behavior of coral aggregate concrete (CAC) under drying-wetting cycles. The influences of the aggregate type, strength grade, fly ash (FA) content, and basalt fiber (BF) content on the free chloride concentration in the concrete were determined. The apparent chloride diffusion coefficient (Dapp) of the CAC was calculated, and then used to analyze the instantaneous chloride diffusion coefficient (Dins) of the CAC. The test results showed that the free chloride concentration of the CAC was higher than that of ordinary aggregate concrete (OAC), with a smaller free chloride concentration for a higher strength grade. The Dapp and Dins first increased and then decreased with increases in the FA content and BF content. The Dins was 65 ~ 87% smaller than the Dapp. The time attenuation coefficient of the chloride diffusion coefficient had good positive correlations with the strength grade and FA content, and a good quadratic functional relationship with the BF content. The peak chloride concentration appeared at approximately 4 mm inside the concrete, and increased with the erosion time, which conformed to the power function law. In addition, a calculation model for the apparent chloride diffusion coefficient was established. The porosity of CAC can be effectively reduced when the FA content is 30% or the BF content is 0.1%, in addition, the chloride diffusion coefficient is positively correlated with the porosity.

A facile approach to prepare a flexible and durable electrically driven cotton fabric-based heater

Flexible and durable electrically driven heaters (EDHs) was prepared by using silver nanowire/polydopamine modified cotton fabric (AgNW/PDA-C) as Joule heat generator and polydimethylsiloxane (PDMS) as stretchable matrix.The electric property of the EDHs was investigated, and it can show excellent electrical property and stability. The EDHs can be seen from the SEM morphology that cotton fabric was well protected by the PDMS and has good conductive network. The EDHs also exhibit excellent electrothermal performance under applied voltage. At low-voltages, it can quickly reach satisfactory steady-state temperatures that meet the needs of wearables. By improving the electrothermal model, it can be verified that there is a quadratic function relationship between electric power and steady-state temperature. Under cyclic voltage and bending tests, the EDHs can well maintain steady-state temperature and exhibit excellent dynamic and static electrothermal performance.

Energy storage and dissipation characteristics of red sandstone in triaxial compression tests under constant confining pressure

To investigate the energy storage and dissipation characteristics of rock material in triaxial compression tests under constant confining pressure, a series of triaxial single-cyclic loading–unloading compression tests were conducted on red sandstone specimens under eight confining pressures. Using the method of graphic area integration, the input energy density, elastic energy density, and dissipative energy density of the specimen in axial, circumferential, and total directions were obtained. The results indicate that the input energy density in the axial direction accounts for the largest logarithmic proportion of the total input energy density and that the relationship between all the parameters of the energy density and the unloading level can be described by the quadratic function. In the axial direction, a linear function relationship exists among elastic, dissipative, and input energy densities. In the circumferential direction, a quadratic function relationship exists among elastic, dissipative, and input energy densities. For the total energy parameters of the sample, the relationship of elastic, dissipative, and input energy densities conforms to the quadratic function, providing a new method for the accurate estimation of the energy parameters in the rock under high stress.

Evolutionary characteristics of mode-I fracture toughness and fracture energy in granite from different burial depths under high-temperature effect

For urgent solutions to existing major engineering problems such as deep mining and deep burial of high level radioactive nuclear wastes, exploring the mechanical behaviors of rocks under the synergistic effect of the burial depth of rocks and temperature is of great significance. The mode-I fracture characteristics of granite specimens in the semi-circular bending (SCB) test under the effects of different temperatures and burial depths were experimental investigated. The test results showed that the mineral compositions and fracture characteristics of granite both varied significantly at different burial depths in Daliuhang Gold Mine in Yantai, Shandong Province, China. The high-temperature effect would remarkably weaken the influence of the burial depth on the fracture characteristics of granite; moreover, increasingly growing temperature gradually became a dominant factor influencing the fracture characteristics of granite. As the temperature rose from 20 °C to 900 °C, the peak strength, fracture toughness and fracture energy of granite at different burial depths all declined with the temperature rise. Additionally, a significant quadratic polynomial function relationship was found in temperature with peak strength and fracture toughness. Additionally, it was macroscopically found that the fracture energy linearly increased with the fracture toughness, implying that the specimens with larger fracture toughness need to consume more energy during the failure. However, the specific proportions and rates of energy consumption differed in different fracture stages of granite.